I recommend getting an orange traffic cone and cutting the small end off. Fasten the cone to a stump or fence post. Put the chicken in the cone head down with the head sticking out. Slit the throat.

Chickens become calm when held upside down like that. And there's no thrashing or running around afterwards. Also, the cutting the throat (or lop the head off, but that's harder) is supposed to be the least traumatic for the chicken.

Just don't let the OTHER chickens see you kill one. It totally stresses them out.